THE SENSITIVITY OF A 3D STREET CANYON CFD MODEL TO UNCERTAINTIES IN INPUT PARAMETERS

1
THE SENSITIVITY OF A 3D STREET CANYON CFD MODEL
TO UNCERTAINTIES IN INPUT PARAMETERS
Energy Resources Research Institute (ERRI)

• James Benson, Nick Dixon, Tilo Ziehn and Alison
  S. Tomlin
• prejfb_at_leeds.ac.uk

2
Overview

• 1. Motivation.
• 2. Case study.
• 3. Model setup.
• 4. Sensitivity analysis.
• 5. Results.
• 6. Conclusions.

3
Motivation

• CFD models increasingly used for prediction of
  air flow in urban areas.
• Individual buildings resolved.
• 3D flow structures are predicted.
• Currently lack of information on computational
  fluid dynamic (CFD) model sensitivity/
  uncertainty.
• Need to
• - Determine effects of lack of knowledge of input
  parameters.
• - Improve confidence in air pollution models.
• - Provide information to help develop pollution
  modelling system.
• Require suitable sensitivity and uncertainty
  analysis techniques.

4
Case Study

• Gillygate, York, UK.
• Typical street canyon. H/W 0.8.
• Site of extensive experimental campaign. (Boddy
  et al. 2005).
• Experimental results allow comparison/ validation
  of CFD model.

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Model

• Model is CFD k-e turbulent flow model MISKAM
  v4.21 (Eichorn, 1996).
• Commonly used as an operation model (Lohmeyer et
  al., 2000).
• Uncertainties exist in input parameters
  including
• - Background wind direction ?.
• - Surface and building roughness lengths.
• - Inflow surface roughness length (determines
  effect of upwind terrain on wind and turbulence
  profiles).
• Interested in effects on predicted flow (u, v, w
  and mean wind speed, U) and turbulence (Turbulent
  Kinetic Energy -TKE) in street canyon.

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Model input parameters

• Surface roughness length z0, used in log-law of
  the wind.
• Inflow, buildings and surface roughness lengths.
• Background wind direction ?
• - To show the effect of misspecification when
  comparing to experimental results.

u horizontal wind velocity u - friction
velocity z distance from surface z0 surface
roughness length ? Von Karman Constant
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Input parameter ranges
Input parameter range
surface roughness length 0.5-50cm
building roughness length 0.5-10cm
inflow roughness length 5-50cm
background wind direction (?) ?10

• Uniform input parameter distributions.
• Ranges chosen based on model limitations and
  modellers experience.

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Model domain grid setup

• Non-equidistant grid.
• Resolution 89 (270m) x 124 (400m) x 28 (100m)
  points.
• Measurement points at
• - G3 (183,211,5.5m), 2m from canyon wall.
• - G4 (171,211,5.3m), 1m from canyon wall.

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Sensitivity Techniques

• Random Sampling Monte-Carlo (RS-MC) with
  regression analysis
• - Pearson correlation coefficient.
• - Spearman ranked correlation coefficient.
• Random-Sampling High Dimensional Model
  Representation (RS-HDMR)
• - First order sensitivity indices.
• - Second order sensitivity indices.
• Cross sectional sensitivity analysis of model
  domain (y211m).
• Comparison to experimental results.

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Monte Carlo sampling sensitivity analysis

• 10000 runs at each wind angle for stable output
  means and variance.
• Random sampling.
• Input parameter limits and distributions defined.
• Samples generated for each parameter from above
  limits.
• Model run using input parameters from samples.
• 30 -40 minutes runtime for each run on 2GHz
  computer
• Time taken for Monte-Carlo runs using single
  desktop PC 625 days.
• Time taken on Everest 30 processors of
  distributed memory computer for 10000 Monte-Carlo
  runs 21 days.

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HDMR Sensitivity Analysis

• Monte Carlo analysis requires large numbers of
  model runs which are often computationally
  prohibitive.
• HDMR is a more effective way of determining
  sensitivities for non-linear models.
• - Input parameter limits and distributions
  defined.
• - Quasi-random samples generated for each
  parameter from above limits.
• - Model run using input parameters from samples.
• - Model replacement constructed from the
  responses of the output to the inputs.
• Model replacement used to generate sensitivity
  indices at much reduced computational cost.
• Time taken on Everest 30 processors for 1024
  HDMR runs 2.1 days.

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Comparison of model results and experimental
field results

• G3 TKE/Um2. Black circles experimental 15 minute
  averages, grey dots RS-MC model results. The
  error bars on the experimental data are 1
  standard deviation from the mean. ? -
  coefficient of variation for the model results.

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Mean TKE model results for ? 9010

• Canyon cross-section of mean TKE and u, w wind
  vectors for ?9010

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Measurement point sensitivity analysis results
G3 TKE at ?9010
Sensitivity method Pearson correlations Pearson correlations Spearman Ranked correlations Spearman Ranked correlations HDMR first order
r r2 rsp rsp2 Si
surface roughness -0.5578 0.3112 -0.5690 0.3238 0.4258
building roughness -0.3091 0.0955 -0.2803 0.0786 0.1154
inflow roughness 0.5131 0.2632 0.5542 0.3071 0.2533
wind direction (?) 0.3689 0.1361 0.3643 0.1327 0.1610
total 0.8060 0.8422 0.9555
Sensitivity of mean TKE at G3 to each parameter
given by Pearson and Spearman Ranked Correlation
coefficients and RS-HDMR first order sensitivity
indices for ?9010.
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HDMR first order component function for G3 TKE at
?9010

• Scatter plot (a) and RS-HDMR component function
  (b) for surface roughness length and
  un-normalised TKE at G3 for ? 9010.

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Measurement point sensitivity analysis results
G3 U at ?9010
G3 U Pearson correlations Pearson correlations Spearman Ranked correlations Spearman Ranked correlations HDMR first order
  r r2 rsp rsp2  Si
surface roughness -0.4924 0.2424 -0.4917 0.2417 0.2833
building roughness -0.1846 0.0341 -0.1968 0.0387 0.0491
inflow roughness -0.1747 0.0305 -0.1651 0.0273 0.0359
wind direction (?) -0.7610 0.5791 -0.7570 0.5731 0.6438
total 0.8861 0.8808 1.0121
Sensitivity of mean wind speed (U) at G3 to each
parameter given by Pearson and Spearman Ranked
Correlation coefficients and RS-HDMR first order
sensitivity indices for ?9010.
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HDMR first order component function for v at G3,
?9010

• Scatter plot (a) and RS-HDMR component function
  (b) for ? and along canyon wind component v at G3
  for ? 9010.

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Measurement point sensitivity analysis results
G3 TKE at ?18010
Pearson correlations Pearson correlations Spearman Ranked Correlations Spearman Ranked Correlations HDMR first order
r r2 rsp rsp2 Si
surface roughness -0.0140 0.0002 -0.0113 0.0001 0.0005
building roughness -0.0247 0.0006 0.0059 0.0000 0.0009
inflow roughness 0.4159 0.1730 0.4495 0.2020 0.1520
wind direction 0.7525 0.5662 0.7320 0.5359 0.7433
total 0.7400 0.7380 0.8967
Parameter interaction HDMR second order Sij
surface roughness wind direction 0.0003
surface roughness building roughness 0.0014
surface roughness inflow roughness 0.0003
building roughness wind direction 0.0205
building roughness inflow roughness 0.0057
wind direction inflow roughness 0.0365
total 0.0647
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Cross section of TKE sensitivity at ?9010
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Cross section of U sensitivity at ?9010
Surface roughness length
Building roughness length
Inflow roughness length
Background wind direction ?
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Sensitivity across all wind angles
Relative sensitivity at (a) G3 and (b) G4 of
un-normalised TKE (m2s-2) to all input parameters
across all background wind angles.? - surface
roughness length,o - building surface roughness
length, ?inflow roughness length, - ?
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Conclusions

• Overall uncertainty is small in comparison to
  model output means even with all possible
  parameter uncertainty included.
• Sensitivity is highly location dependant.
• Sensitivity is highly wind direction dependant.
• HDMR method provides more detailed sensitivity
  information including non-linear and second order
  effects with reduced computational expense.

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Acknowledgements

• Thanks to ERSPC for the project funding and the
  EC for supporting this presentation at SAMO 2007.
• Also thanks to A. Tomlin, T. Ziehn and N. Dixon.